I didn't follow some portions of your question, and hopefully you take this well :).
"I am also considering creating a native app similar to CakePhp or Node.js" --> There are three separate concepts in there that are worth unwrapping, so probably good to talk about that first:
CakePHP is a PHP framework, comparable to Symfony/Laravel/CodeIgniter/etc.
Node.js is a JavaScript language & runtime, comparable to PHP, Python, Ruby, .NET, etc. Similar to Cake/Laravel/etc, there are many great frameworks in Node.js; Express, Meteor as you mention (well, Meteor is more of a tapestry of many technologies, and it's awesome!).
Native apps are usually iOS, Android, Windows, etc, but can be hybrid, too (Ionic, Phonegap, React Native, etc). Connected native applications usually have a backend, which is usually written in a language like the ones mentioned above, and usually with a framework written on top of it to accelerate development.
With that out of the way, let's tackle the main meat of your question:
Can PHP be used to create a platform similar to AirBnB, Ebay, Amazon?
Answer: Absolutely!!! Just one recent example is Slack, who's backend is build on PHP (LAMP stack). Check out this tweet where they mention their stack: https://twitter.com/SlackHQ/status/426469205005705217. Another good discussion on it: https://www.quora.com/What-web-framework-s-does-Slack-run-on.
One bottom line is that choosing a technology stack is important, but more importantly is the correct and effective development on the chosen technologies. I've seen both beautiful and horrible applications written in most languages. Much care needs to be spent architecting and developing the solution, always using best practices, and considering what's the right decision for the business at hand (hint: there's no silver bullet).
My suggestion: choose whatever you're more comfortable with. Also, surround yourself with someone that has created something of the magnitude of what you're aiming for, and ask for advice.
Now, for a opinionated answer: I'm currently building most highly-scalable backends on Node.js + some kind of framework. The frontend is, in most cases, being built using a client-side Javascript framwork such as React or Angular - this is assuming it's going to be heavy client side, which means that one can spin up a native app using hybrid methods. There are many cases, though, where we're building native apps, too. Again, this depends on the business case for a particular choice.
Happy to jump on a call, show you some examples of this, and answer any questions you have!
